Algebra Basics Quiz

Solving Linear Equations

• The equation $3x + 7 = 16$ can be solved for $x$ by isolating the variable.
• Subtract 7 from both sides to obtain $3x = 9$.
• Divide both sides by 3 to get $x = 3$.

Calculating Triangle Area

• The formula for the area of a triangle is $A = \frac{1}{2}bh$, where $b$ is the base and $h$ is the height.
• Substitute $b = 10$ and $h = 5$ into the formula: $A = \frac{1}{2}(10)(5)$.
• Simplify to get $A = 25$.

Identifying Slope

• The equation $y = 4x + 2$ is in slope-intercept form ($y = mx + c$), where $m$ represents the slope.
• Therefore, the slope of the line is $m = 4$.

Understanding Quadratic Roots

• The product of the roots of a quadratic equation in the form $ax^2 + bx + c = 0$ is given by $c/a$.
• In the equation $x^2 - 5x + 6 = 0$, the product of the roots $p$ and $q$ is $(6)/(1) = 6$.

Finding Derivatives

• The derivative of a function $f(x) = x^n$ is given by $f'(x) = nx^{n-1}$.
• Applying this to the function $f(x) = x^3 - 3x^2 + 4$, we get the derivative $f'(x) = 3x^2 - 6x$.